Steady state temperature profile in a sphere heated by microwaves

A new theory has been developed to calculate the microwave absorption and resultant temperature profile within a sphere positioned in a single mode rectangular cavity. This theory is an extension of a total absorption model based on Mie scattering results. Temperature profiles have been computed for alumina spheres at the center of a rectangular cavity excited in the TM354 mode. Parametric studies reveal significant structure in those profiles under special conditions that are associated with electromagnetic resonances inside the spheres. Anomalous behavior similar to thermal runaway occurs at moderate temperatures when there is enhanced absorption associated with resonant conditions in the sphere.